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Physics in Nuclear Medicine Physics in Nuclear Medicine James A. Sorenson, Ph.D. Professor of Radiology Department of Radiology University of Utah Medical Center Salt Lake City, Utah Michael E. Phelps, Ph.D. Professor of Radiological Sciences Department of Radiological Sciences Center for Health Sciences University of California Los Angeles, California ~ J Grune & Stratton A Subsidiary of Harcourt BraceJovanovich, Publishers New York London Paris San Diego San Francisco Sao Paulo Sydney Tokyo Toronto Radioactivity is a process involving events in individual atoms and nuclei. Before discussingradioactivity, therefore, it is worthwhile to review some of the basic conceptsof atomic and nuclearphysics. A. MASS AND ENERGY UNITS Events occurring on the atomic scale, such as radioactivedecay, involve massesand energiesmuch smaller than those encounteredin the eventsof our everydayexperiences. Therefore they are describedin termsof massand energy units more appropriateto the atomic scale. The basic unit of massis the universal massunit, abbreviatedu. One u is defined as being equal to exactly Y12the mass of a 12C atom. t A slightly different unit, commonly used in chemistry, is the atomic mass unit (amu), basedon the averageweight of oxygen isotopesin their natural abundance.In this text, except where indicated, masseswill be expressedin universal mass units, u. The basic unit of energy is the electron volt, abbreviatedeV. One eV is defined as the amount of energy acquiredby an electronwhen it is accelerated through an electrical potential of one volt. Basic multiples are the keV (kilo electron volt; 1 keY = 1000 eV) and the MeV (Mega electron volt; 1 MeV = 1000 keY = 1,000,000eV). Mass m and energy E are related to each other by Einstein's equationE = mc2,where c is the velocity of light. According to this equation, 1 u of mass is equivalentto 931.5 MeV of energy. tAtomi~ notation is discussedin SectionD.2 of this chapter. 1 2 Physics in Nuclear Medicine Table 1-1 Mass and Energy Units , I -.. Multiply - To Obtain To Obtain By 4i-- Divide u 1.66043 X 10-24 g u 4.86 X 10-26 oz u 1.00083 amu eV 1.6021 X 10-12 ergs eV 3.83 X 10-20 g.cal u 931.478 MeV Relationships between various units of mass and energy are summarized in Table 1-1. Universal mass units and electron volts are very small, yet, as we shall see, they are quite appropriate to the atomic scale. B. ELECTROMAGNETIC RADIATION (PHOTONS) Atomic and nuclear processes often result in the emission of electromag- netic radiation, such as x rays (Section C.3), and -y rays (gamma rays, Section D.5). Electromagnetic radiation consists of oscillating electrical and magnetic fields traveling through space with the velocity of light, c (approximately 3 X 108 meters/sec in vacuum). The wavelength A and frequency v of these oscillating fields are related by AV = C (1-1) In some cases, e.g., when interacting with atoms, electromagnetic radia- tions behave as discrete "packets" of energy, called photons (also called quanta). A photon is a packet of electromagnetic energy having no mass or electrical charge that also travels through space at the velocity of light. The energy of a photon, E, and the wavelength A of its associated electromagnetic field are related by E(keV) = l2.4/A(A) (1-2) A(A) = l2.4/E(keV) (1-3) Table 1-2 lists approximate photon energies and wavelengths for different parts of the electromagnetic spectrum. Note that x and -y rays occupy the highest- energy, shortest-wavelength end of the spectrum; x- and -y-ray photons have energies in the keY-MeV range, whereas visible light photons, for example, have energies of only a few eV. As a consequence of their short wavelength Basic Atomic and Nuclear Physics 3 Table 1-2 ApproximatePhoton Energy and Wavelength Ranges for DifferentTypes of ElectromagneticRadiation Type Energy(eV) Wavelength Radio,TV, radar 10-9-10-3 10-I-I0~ cm Infrared 10-3-2 10-4-10-1cm Visible 2-3 4000-7000At Ultraviolet 3-25 50-4000A x rays 25-105 10-1-50A 'Yrays 104-106 10-2-1 A tl A = 10-8Cffi. and high energy, x and 'Y rays interact with matter quite differently from other, more familiar types of electromagneticradiation. These interactions are dis- cussedin detail in Chapter9. C. ATOMS 1. Composition and Structure All matter is comprisedof atoms. An atom is the smallestunit into which a chemical element can be broken down without losing its chemical identity. Atoms combine to form molecules and chemical compounds, which in turn combineto form larger, macroscopicstructures. The existenceof atoms was first postulatedon philosophical grounds by Ionian scholarsin the 5th century B.C. The conceptwas formalized into sci- entific theory early in the 19thcentury, owing largely to the work of the chemist Dalton and his contemporaries.The exact structureof atoms was not known, but at that time they were believedto be indivisible. Later in the century (1869), Mendeleevproduced the first periodic table, an ordering of the chemical ele- ments according to the weights of their atoms and arrangementin a grid ac- cording to their chemicalproperties. For a time it was believedthat completion of the periodic table would representthe final stepin understandingthe structure of matter. Events of the late 19th and early 20th centuries,beginning with the dis- covery of x rays by Roentgen(1895) and radioactivity by Bequerel (1896), revealedthat atoms had a substructureof their own. In 1910, Rutherford pre- sentedexperimental evidence indicating that atoms consisted of a massive, compact,positively chargedcore, or nucleus,surrounded by a diffuse cloud of relatively light, negativelycharged electrons. This model cameto be known as the nuclear atom. The number of positive chargesin the nucleusis called the atomic number of the nucleus(Z). In the electrically neutral atom, the number of orbital electrons is sufficient to balance exactly the number of positive 4 Physics in Nuclear Medicine charges,Z, in the nucleus.The chemicalproperties of an atom are determined by orbital electrons;therefore the atomic number Z determinesthe chemical elementto which the atom belongs. A listing of chemical elementsand their atomic numbersis given in Appendix A. According to classicaltheory, orbiting electronsshould slowly lose energy and spiral into the nucleus, resulting in atomic "collapse." This is qbviously not what happens.The simple nuclear model therefore neededfurther refi~e- ment. This was provided by Niels Bohr in 1913, who presenteda model that has come to be known as the Bohr atom. In the Bohr atom there is a set of stableelectron orbits or "shells" in which electronscan exist indefinitely with- out loss of energy. The diametersof these shells are determinedby quantum numbers,which canhave only integervalues (n = 1, 2, 3, . .). Theinnermost shell (n = 1) is called the K shell, the next the L shell (n = 2), followed by the M shell (n = 3), N shell (n = 4), and so forth. Each shell is actually comprisedof a set of orbits, called substates,which differ slightly from one another.Each shell has 2n - 1 substates,where n is the quantum number of the shell. Thus the K shell has only one substate;the L shell has three substates,labeled L1, LII' LIII; and so forth. Figure 1-1 is a schematicrepresentation of the K and L shells of an atom. The M shell and other higher shells have larger diameters. The Bohr model of the atom was further refined with the statementof the Pauli Exclusion Principle in 1925. According to this principle, no two orbital electronsin an atom can move with exactly the samemotion. Becauseof dif- ferent possible electron "spin" orientations,more than one electron can exist in each substate(Figure 1-1); however, the number of electronsthat can exist in anyone shell or its substatesis limited. For a shell with quantumnumber n, THE BOHRATOM ~ :~~ ;;;;==--~:: ~ ~ ij - - " " "~ ((I t ::::~:~:. ',\ '\\\)) ~\ \, ", NUCLEUS i I \\:~ "' -<~' /( Ij ---~t.\..\..' ~/~/ ~",~~ KS .~/ ' ' ::-- ~~-=---~... --~~- L SHELL,n=2 Fig. 1-1. SchelIlatic representation'of the Bohr lIIodel of the atom; n is the quantumnumber of the shell. The K shell has one substateand the L shell has three substates.Each substatehas two electrons. Basic Atomic and NuclearPhysics 5 the maximum number of electrons allowed is 2n2. Thus the K shell (n = 1) is limited to two electrons, the L shell (n = 2) to eight electrons, and so forth. The Bohr model is actually an oversimplification. According to modem theories the orbital electrons do not move in precise circular orbits, but rather in imprecisely defined "regions of space" around the nucleus, sometimes ac- tually passing through the nucleus; however, the Bohr model is quite adequate for the purposes of this text. 2. Electron Binding Energies and Energy Levels In the most stable configuration, orbital electrons occupy the innermost shells of an atom, where they are most "tightly bound" to the nucleus. For example, in carbon, which has six electrons, two electrons (the maximum num- ber allowed) occupy the K shell, and the four remaining electrons are found in the L shell. Electrons can be moved to higher shells or completely removed from the atom, but doing so requires an energy input to overcQme the forces of attraction that "bind" the electron to the nucleus. The energy may be pro- vided, for example, by a particle or a photon striking the atom. The amount of energy required to completely remove an electron from a given shell in an atom is called the binding energy of that shell. It is symbolized by the notation KB for the K shell,t LB for the L shell (LIB' LIIB' LIIIB for the L shell substates), and so forth. Binding energy is greatest for the innermost shell; i.e., KB > LB > MB. Binding energy also increases with the positive charge (atomic number Z) of the nucleus, since a greater positive charge exerts a greater force of attraction on an electron.
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